To determine the direction of the velocity of the plane relative to the ground, we need to use vector addition. The plane is flying in the y-direction at 190 m/s, and the wind is blowing in the x-direction at 25.0 m/s. The resultant velocity vector is a combination of these two vectors.
Let's denote:
- \( V_p \) as the velocity of the plane (190 m/s in the y-direction).
- \( V_w \) as the velocity of the wind (25.0 m/s in the x-direction).
The direction \(\theta\) of the resultant velocity relative to the positive x-axis (wind direction) can be found using trigonometry, particularly the tangent function:
\[ \tan(\theta) = \frac{V_p}{V_w} \]
Plugging in the given values:
\[ \tan(\theta) = \frac{190 \, m/s}{25.0 \, m/s} \]
Solving for \(\theta\):
\[ \theta = \arctan\left(\frac{190}{25.0}\right) \]
\[ \theta = \arctan(7.6) \]
Using a calculator to find the arctangent of 7.6:
\[ \theta \approx 82.5^\circ \]
Therefore, the direction of the velocity of the plane relative to the ground is approximately \(82.5^\circ\) north of east (or from the positive x-axis towards the positive y-axis).
a plane is flying at 190 m/s in the y-direction. The wind is blowing at 25.0 m/s in the x-direction. What is the direction of the velocity of the plane?
0=[?]degrees
1 answer